1. Field of the Invention
The present invention relates to a diffraction element used in a spectrometer which is used for spectral analysis for a light beam (light), a manufacturing method (processing method) for a diffraction element, and a spectrometer using the same.
Further, the present invention relates to a color image forming apparatus which uses the spectrometer using the diffraction element so as to perform spectral analysis for an output image.
2. Description of the Related Art
Most conventional spectrometers use a diffraction element. In particular, there is provided a well-known compact spectrometer having a structure in which a slit is disposed at an arbitrary position on the Rowland circle of a concave diffraction element (see Japanese Patent Application Laid-Open No. H05-340813 and Japanese Patent Application Laid-Open No. 2007-333581).
Note that the concave diffraction element means a diffraction element formed so that a substrate on which the diffraction grating is formed has a concave surface.
FIG. 18 is a principal part cross sectional view of this type of spectrometer in a spectral direction.
In FIG. 18, a light beam entering through an incident slit 101 is diffracted by a concave diffraction element 102 having fine grooves formed in a direction perpendicular to the paper face in different angles for respective wavelengths, which are condensed on a one-dimensional array light detector 103 such as a CCD. Then, intensity values of light beams entering individual light receiving elements of the one-dimensional array light detector 103 are measured so that spectral measurement is performed.
Here, the Rowland circle is defined as a circle that passes through the center of the concave diffraction element 102 and has a diameter set as a curvature radius thereof. A circle drawn by a dotted line denoted by reference numeral 104 is the Rowland circle.
The light beam entering through the incident slit 101 on the Rowland circle 104 is reflected and diffracted by the concave diffraction element 102, and then forms an image on the Rowland circle 104.
Therefore, the incident slit 101 and the light detector 103 are disposed on the Rowland circle 104 so as to perform the spectral measurement with high accuracy.
The concave shape of the concave diffraction element 102 that is used for the conventional spectrometer is usually set as a spherical surface. Imaging states on the light detector 103 in this case are illustrated in FIGS. 19 and 20.
FIG. 19 is a diagram illustrating an imaging state in a cross section in the spectral direction from the incident slit 101 to the light detector 103.
Note that FIG. 19 representatively illustrates an imaging state of a light beam of a specific wavelength that is reflected and diffracted by the concave diffraction element 102.
Because the light detector 103 is disposed on a part of the Rowland circle 104, in the cross section in the spectral direction, the reflected and diffracted light beam forms an image appropriately on the light detector 103.
On the other hand, FIG. 20 is a diagram illustrating an imaging state in a cross section in the direction orthogonal to the spectral direction from the concave diffraction element 102 to the light detector 103, i.e., in the direction in which the grooves of the diffraction grating extend.
Similarly to FIG. 19, FIG. 20 representatively illustrates an imaging state of a light beam of a specific wavelength that is reflected and diffracted by the concave diffraction element 102.
In the cross section illustrated in FIG. 20, the reflected and diffracted light beam does not form an image on the light detector 103 but forms an image at a position far from that of the light detector 103 when viewed from the concave diffraction element 102.
This is because the light beam reflected and diffracted by the concave diffraction element 102 and the line connecting a contact point A of the concave diffraction element 102 and the Rowland circle 104 with a center point A′ of the Rowland circle forms a predetermined angle φ in the case of FIG. 19, while the light beam and the line do not form the angle in the case of FIG. 20.
Because measurement accuracy of the spectrometer depends on imaging performance in the spectral direction illustrated in FIG. 19, the light detector 103 may be disposed on the Rowland circle 104 or in its vicinity.
Therefore, there is a malfunction that the light beam is not naturally condensed in the direction orthogonal to the spectral direction, and intensity values of the light beams entering the light receiving elements of the light detector 103 are lowered.
In order to prevent the malfunction, the concave shape of the concave diffraction element 102 only needs to be set so that the curvature radius in the cross section orthogonal to the spectral direction illustrated in FIG. 20 is smaller than the curvature radius in the cross section in the spectral direction illustrated in FIG. 19.
In other words, if the shape of the concave diffraction element 102 is set to have an anamorphic toric surface, the above-mentioned malfunction may be resolved.
Hereinafter, the above-mentioned toric surface is described with reference to FIG. 21.
In FIG. 21, with respect to the concave diffraction element 102, a rectangular coordinate system is defined so that the cross section in the spectral direction illustrated in FIG. 20 corresponds to the xy plane while the cross section in the direction orthogonal to the spectral direction illustrated in FIG. 20 corresponds to the zx plane.
Here, the concave shape of the concave diffraction element 102 is set so that a curvature radius r in the cross section (in the zx plane) in the direction orthogonal to the spectral direction (y direction) is smaller than a curvature radius R in the cross section (in the xy plane) in the spectral direction. From this fact, it is considered that the concave shape of the concave diffraction element 102 is set as a so-called general toric surface in which an arc having the curvature radius r is rotated about the z axis as a rotation axis along an arc having the radius R.
In this specification, the above-mentioned general toric surface is referred to as a “z-toric surface” hereinafter.
In addition, the spectral direction of the concave diffraction element 102 is in the xy plane illustrated in FIG. 21. Therefore, gratings of the diffraction grating on the concave diffraction element 102 form lines parallel to the z axis when the concave diffraction element 102 is viewed from the X-axis direction shown in FIG. 21.
A specific pattern of a diffraction grating 201 formed on the concave diffraction element 102, which is viewed from X-axis direction shown in FIG. 21, is illustrated in FIG. 22.
In addition, in order to improve diffraction efficiency of the concave diffraction element 102, in general, the diffraction grating of the concave diffraction element 102 may be a blazed grating.
FIG. 23 is a diagram illustrating a structure of the diffraction grating (blazed grating) 201 in the cross section (XY section) in the spectral direction of the concave diffraction element 102.
In FIG. 23, incident light entering the concave diffraction element 102 is reflected and diffracted by the diffraction grating 201. In this case, if a first-order diffracted light is used for the spectral analysis, the blazed grating 201 as illustrated in FIG. 23 is used, and an oblique surface 202 of the diffraction grating 201 is inclined to the direction in which the first-order diffracted light is reflected and diffracted so that diffraction efficiency in the first-order diffracted light may be improved.
Next, a processing method (manufacturing method) of the blazed grating 201 illustrated in FIG. 23 is described.
FIG. 24 is a diagram illustrating a manner of processing (manufacturing) the blazed grating 201 illustrated in FIG. 23.
In FIG. 24, the concave diffraction element 102 is processed by cutting work using a turning tool 205 including a super hard tip or single crystal diamond tip 204 fixed to the end of a shank 203 by brazing or the like.
The shank 203 of the turning tool 205 is fixed to a main shaft of NC machine tools (not shown) and is driven to rotate about a rotation axis 206 of the main shaft so that the blazed grating 201 having a blazed angle θ is processed by cutting work so as to have a desired shape by fly-cutting processing.
Note that the main shaft of the NC machine tools or the concave diffraction element 102 is moved in the direction perpendicular to the paper face, so as to form the diffraction grating 201 having lines parallel to the z axis as illustrated in FIG. 22, when viewed from X-axis direction shown in FIG. 21.
However, when the diffraction grating 201 is processed on the “z-toric surface” as illustrated in FIG. 21, the following problem occurs.
FIG. 25 illustrates a schematic view of the processing of the diffraction gratings on the z-toric surface at the point P which is in the xy plane with z=0. When processing the diffraction gratings at the point P, the rotation axis 206 of the main shaft for rotating the turning tool 205 exists in xy plane. And if the main shaft for rotating the turning tool 205 is rotated about a straight line M which is orthogonal to the straight line L connecting the origin O and the point P and exists in xy plane, the diffraction grating can be formed on the z-toric surface as a line N illustrated in FIG. 25.
If the diffraction gratings are formed in this manner, the rotation axis 206 of the main shaft for rotating the turning tool 205 and the direction of the movement of the turning tool 205 are constantly orthogonal to each other. Therefore, the diffraction gratings N can be formed by fly-cutting processing to have a desired section form as blazed gratings constantly having a blazed angle θ shown in FIG. 24 at any point.
FIG. 26 shows the diffraction gratings viewed from X-direction where the diffraction gratings are formed by the method described above. As can be understood from FIG. 26, if the diffraction gratings are observed from the X-axis direction, the diffraction gratings can be observed as curved lines concave to the origin point side except a diffraction grating on a xz plane with y=0 which can be observed as a straight line.
This is because the diffraction gratings are formed by rotating the rotation axis 206 of the main shaft for rotating the turning tool 205 about a straight line M which is orthogonal to the straight line L connecting the origin O and the point P and exists in xy plane. All the diffraction gratings formed in this manner can be observed as straight lines only when viewed from the origin O.
A spectroscopic analysis by use of the diffraction gratings illustrated in FIG. 26 causes a problem in which the precision in spectroscopy is deteriorated due to the difference in pitch of the diffraction gratings depending on the distance from the xy plane with z=0 as can be understood from FIG. 26.
Therefore, the diffraction gratings generally need to be formed to be parallel to each other and to have the same interval therebetween when viewed from X-axis direction as illustrated in FIG. 22.
Diffraction gratings N which are formed on the z-toric surface shown in FIG. 25 and can be observed as straight lines when viewed from X-axis direction, can be observed as illustrated in FIG. 27 when viewed from the origin O. So, if the diffraction gratings are formed so that the diffraction gratings can be observed not as straight lines but as curves convex to the origin side when viewed from the origin O as shown in FIG. 27, the formed diffraction gratings can be observed as straight lines when viewed from X-axis direction. This can be readily understood from a simple geometric consideration.
Such processing of the diffraction gratings cannot be performed by the method described with reference to FIG. 25 but can be performed by a method which will be described below with reference to FIG. 28. The rotation axis 206 of the main shaft for rotating the turning tool 205 is in xy plane when processing the diffraction grating at the point P as illustrated in FIG. 28. The diffraction gratings illustrated in FIG. 27 can be formed by rotating the rotation axis 206 of the main shaft for rotating the turning tool 205 about a straight line M which is orthogonal to the straight line L connecting the origin O and the point P and is in xy plane and simultaneously by moving the rotation axis 206 of the main shaft in the Y-axis direction.
However, in a diffraction gratings formed by such processing, at any point except the point P, since the rotation axis 206 of the main shaft for rotating the turning tool 205 and the movement direction of the turning tool 205 are not orthogonal to each other, the wall portion 207 of the diffraction grating shown in FIG. 24 is cut out by the rotation of the turning tool 205 so that the wall portion 207 is not formed perpendicularly.
FIG. 29 shows a schematic diagram of the processing of the diffraction grating at point Q apart from the point P in the z-axis direction (see FIG. 27). The turning tool 205 is rotated about the rotation axis 206 to thereby perform the fly-cutting processing of the diffraction gratings. When processing the diffraction grating at the point Q, the turning tool 205 is moved in the direction indicated by an arrow illustrated in FIG. 29 (in the tangential direction of the wall portion 207 of the diffraction grating). As a result, since the rotation axis 206 of the main shaft for rotating the turning tool 205 and the movement direction of the turning tool 205 are not orthogonal to each other, the wall portion 207 of the diffraction grating is cut out by the rotation of the turning tool 205 so that the wall portion 207 is not formed perpendicularly.
FIG. 30 is a cross sectional view of the diffraction grating processed in the state as illustrated in FIG. 29.
Because the locus of the wall portion 207 of the diffraction grating 201 (i.e., movement direction of the turning tool 205) is not orthogonal to the rotation axis 206 of the main shaft for rotating the turning tool 205, the wall portion 207 of the diffraction grating 201 is cut out by the rotation of the turning tool 205 as illustrated in FIG. 30.
In this way, if the concave shape of the conventional concave diffraction element 102 is set as the so-called general toric surface (“z-toric surface”) so as to form an image appropriately in both the spectral direction and the direction orthogonal to the spectral direction, the following problem occurs. As a processing problem, the wall portion 207 of the diffraction grating 201 does not have a desired shape, and hence diffraction efficiency is lowered. Further, undesired diffracted light increases, and hence a problem of flare or the like occurs.